Tài liệu hay dành cho giáo viên toán và học sinh tham khảo . Nội dung sách gần với chương trình toán lớp 6 của VN. Nhiều cách tiếp cận hay, nhẹ nhàng giúp học sinh hứng thú và học toán một cách tự nhiên. Nhiều ví dụ minh hoạ, bài tập thực hành hay, gần gũi với cuộc song hàng ngày. Hình vẽ, màu sắc bắt mắt,... Tài liệu giúp giáo viên toán có thêm nguồn tham khảo để hoàn thiện phương pháp giảng dạy, bên cạnh đó cũng giúp giáo viên phát triển vốn tiếng anh, rèn luyện kỹ năng dạy toán song ngữ cho học sinh. Sách hơn 500 trang,..
Trang 2Sadlier-Oxford
A Division of William H
Sadlier, Inc
New York, NY 1002
Trang 3AUDIO GLOSSARY
From A to Z Find the meanings and hear the pronunciations
of math words and phrases.
ALTERNATIVE TEACHING MODELS
Tutorials Watch and listen to these animated math lessons
VIRTUAL MANIPULATIVES
Manipulatives Practice and model math concepts with virtual manipulatives.
PRACTICE
Problem of the Day Tackle a new problem every day!
Skills Update Review your skills with Lesson and Practice pages.
Math Minutes Race against the clock with timed activities!
Practice Activities Practice makes perfect with these fun activities!
Vocabulary Activities Review your math vocabulary while playing Hangman or Word Scramble
ENRICHMENT
Activities Challenge yourself with these interactive activities.
MATH ALIVE AT HOME
Take-Home Activities Share your math experience at home!
Trang 4# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Grade home Glossary home
www.progressinmathematics.com
Choose the fi rst letter of a term you want to review
1
Click on the term
2
Listen as the glossary pronounces the word
If you are not sure what a certain word means or how
to pronounce it, use your online Audio Glossary The glossary is easy to use Just choose your grade level and the fi rst letter of the term you want to review
INTERACTIVECOMPATIBLE
AUDIO LEARNING
Trang 5Red Team Blue Team Green Team
www.progressinmathematics.com
INTERACTIVECOMPATIBLE
VISUAL LEARNING
Trang 6Virtual Manipulatives are
visual models that you
can actually move or
manipulate to show what
is happening You can
use these tools to build
numbers, rotate shapes,
and even jump on a
number line.
Select your grade and the
chapter you are working
on The manipulatives
that are listed will be
ones that you can use to
visualize the concepts of
the chapter.
VIRTUAL MANIPULATIVES
SGT 5
INTERACTIVECOMPATIBLE
Trang 7GRADE 5
PRACTICE
Click Practice Activities.
There is an interactive activity for
each chapter in your textbook
The activity practices the most
important skills of the chapter
Use the activity while you are
learning the skills, or come back
to it later to review.
Click Math Minutes.
You can practice your basic facts
as well as compute with larger
numbers to see how accurately
you can compute if you are given
a time limit
Click Vocabulary Activities.
In each chapter, you will be
learning new math terms that
you will need to know A good
way to review these terms is to
play either the Hangman game
or Word Scramble in your online
INTERACTIVE LEARNING
Trang 8GRADE 6
GRADE 3
*Whiteboard projectable only. GRADE 3
ENRICHMENT
Click Skills Update.*
Print Skills Update lessons
and practice pages to review
previously taught math skills
and concepts.
Click Activities.
The Enrichment activities
online are topics that go
beyond what you are learning
in class.
Each activity starts with a page
that explains the concept and
then gives you time to practice
Click Problem of the Day.*
Sharpen your
problem-solving skills every day
Print and solve one
problem each day!
INTERACTIVECOMPATIBLE
Trang 9Dear Family,
Today our class began Chapter 1 We will learn about place value Let’s dothe activity below together so I can review the skills I will need in order tounderstand the math in this chapter Then we can read some of the newvocabulary I will learn in Chapter 1.
Love,
How Many Tens, How Many Ones?
With your child, list the age of everyone in your family
on a sheet of paper Ask your child to say how many tens and how many ones there are in each age.
Draw a frame like the one at the right for each family member Tell your child to write in each frame the number of tens and ones for each age Then have her/him write an addition with the number of tens and the number of ones for each age, and find the sum.
expanded form shows the place value of the digits
in a number
600 ⫹ 40 ⫹ 7 standard form 647 thousand
nearest ten the number achieved after rounding
to the nearest ten
nearest hundred the number achieved after rounding
to the nearest hundred
We explored patterns of skip counting with 2s, 3s, 4s, 5s, and 10s, whichwill help us to learn multiplication facts We practiced rounding 3- and4-digit numbers to the nearest ten, hundred, or thousand This sk
ill is necessary for estimating with numbers We also worked with money,which will help us make and count change.
Love,
Key Skills and Concepts
Students’ learning in Chapter 1 was guided by giving particular emphasis to the following key skills and concepts:
cano Este conocimiento es necesario para hacer estimaciones con números.Tambiénpracticamos con dinero, lo cual nos ayudará a la hora de dar o recibir cambio.
Con cariño, _
Destrezas y conceptos claves
U l it i i i d l id l d iñ t d
Lo que aprendieron los estudiantes en el capítulo 1 se hizo poniendo énfasis
en las siguientes destrezas y conceptos claves:
Keep your family involved in
what you are learning For
each chapter, there are two
letters to your family Use the
fi rst letter at the beginning
of the chapter, to review
previously learned skills with
a family activity, and read
about the new skills you will
learn The second letter tells
your family about the skills you
learned in the chapter and has
another fun activity that you
and your family members can
Trang 10Tim Mason
Title 1 Specialist Palm Beach County School District
West Palm Beach, FL
Lucy Lugones
Math Coordinator
St Luke’s School Whitestone, NY
Rosalie Pedalino Porter
Consultant Bilingual/ESL Programs
Amherst, MA
Trang 11Copyright © 2009 by William H Sadlier, Inc All rights reserved
This publication, or any part thereof, may not be reproduced in any form, or by any means, including electronic,
photographic, or mechanical, or by any sound recording system, or by any device for storage and retrieval of information, without the written permission of the publisher Address inquiries to Permissions Department, William H Sadlier, Inc.,
9 Pine Street, New York, NY 10005-1002.
is a registered trademark of William H Sadlier, Inc.
Printed in the United States of America
St Louis, MO
Debra WrightPrincipal Winter Haven, FL
John PalladinoProfessor at Eastern Michigan University
Ypsilanti, MI
Marie BicsakMath Coordinator
Mt Clemens, MISuzanne RyanGrade 4 Teacher Orono, MNBrandy RothGrade 3 Teacher Kissimmee, FLBarbara MurphyGrade 4 Teacher Chesterfield, MO
Sr Maristella Dunlavy, O.P
Principal Springfield, IL
Sara KobylarzGrade 3 Teacher Bronx, NYCandace GovinGrades 4– 8 Math Teacher/Coordinator
Plantation, FLElizabeth M JohnsonGrade 5 Teacher Bettendorf, IA
Sr Martha Carmody, O.P
Grade 4 Teacher Springfield, ILJeannine FreyGrade 3 Teacher Chesterfield, MO
Br Ralph Darmento, F.S.C.Deputy Superintendent of Schools
Newark, NJ
Sr Adriana CernochGrade 6 Teacher Dallas, TXLinda HambyGrade 5 Teacher DesPeres, MOJacqueline A ByrdGrade 5 Teacher Chesterfield, MOMary E StokesGrade 5 Teacher Oak Forest, IL
The publisher gratefully acknowledges Rose Anita McDonnell (1905–2003) and her colleagues for the important role they played in the development of
Progress in Mathematics for more than sixty years.
Grades 3–6 Reviewers
Grade-Level Reviewers
Judith A DevineEducational Consultant Springfield, PA
Stephanie D GarlandEducational Consultant
St Louis, MO
RRDW
Trang 12Progress in Mathematics, now in its sixth decade of user-proven success,
is a complete basal mathematics program Written by experienced authors, it integrates a traditional course of study and today’s academicStandards with the most up-to-date methods of teaching
teacher-Progress in Mathematicsis designed to meet the individual needs of all
learners Teachers who use Progress come to understand that students
may progress as quickly as they can or as slowly as they must
In Grade 6, the concepts of integers and rational numbers will be furtherdeveloped as well as ratios, percents, and coordinate geometry There will
be an increased emphasis on algebraic thinking Other topics that arestudied include: data and statistics, probability, geometry, measurement,and proportions Special attention is given to critical thinking, problemsolving, mental math, and journalizing
But overall success in achieving the goals of this program depends onongoing teacher-family-student interaction It is important for you toencourage your sixth grader to achieve success in mathematics and enjoy
it as well You can help your student see math as useful and practical byrelating it to everyday situations It is also helpful to provide a quiet spaceand time for homework, and to reinforce the idea that by practicing mathconcepts and skills in your home environment, your student can have funwhile learning mathematics
Throughout the school year, you and your student can access
pages include the math vocabulary of each chapter plusfun-filled activities that will help you relate the math yourstudent is learning in school to the real world
We know that by usingProgress in Mathematics
your sixth grader will not only learn to value math,but become a confident problem solver and
learn to reason and communicatemathematically as well
Trang 13I Whole Numbers: Place Value,
Compare, and Order 1
II Round Whole Numbers 2
III Factors, Multiples, and Divisibility 3
III Inverse Operations 7
IV Properties of Addition and
I Metric Units of Length 20
II Metric Units of Capacity
and Mass 21
III Customary Units of Length 22
IV Customary Units of Capacity
and Weight 23
V Read an Inch Ruler 24
VI Perimeter and Area
Trang 14Multiplication: Whole Numbers and Decimals
Chapter Opener 65
2-1 Multiplication Patterns 66
2-2 Estimate Products 68
2-3 Multiply Whole Numbers 70
2-4 Multiply with Decimals 72
2-5 Exponents 74
2-6 Scientific Notation 76
2-7 Problem-Solving Strategy: Use Simpler Numbers 78
2-8 Problem-Solving Applications: Mixed Review 80
End of Chapter Check Your Progress (Lessons 1–8) 82
Enrichment: Square Roots 83
Chapter 2 Test 84
Cumulative Review 85
Chapter Number Sense, Addition, and Subtraction Chapter Opener 33
1-1 Place Value 34
1-2 Expanded Form 36
1-3 Place Value and Exponents 38
1-4 Compare and Order Decimals 40
1-5 Round Whole Numbers and Decimals 42
1-6 Estimate Decimal Sums and Differences 44
1-7 Addition of Whole Numbers and Decimals 46
1-8 Subtraction of Whole Numbers and Decimals 48
1-9 Addition and Subtraction of Decimals 50
1-10 Addition and Subtraction Expressions 52
1-11 Evaluate Addition and Subtraction Expressions 54
1-12 Problem-Solving Strategy: Write an Equation 56
1-13 Problem-Solving Applications: Mixed Review 58
End of Chapter Check Your Progress (Lessons 1–13) 60
Enrichment: Roman Numerals 61
Chapter 1 Test 62
Cumulative Review 63
Trang 15Chapter
Division: Whole
Numbers and Decimals
Chapter Opener 87
3-1 Short Division 88
3-2 Estimate Quotients 90
3-3 Divide Whole Numbers 92
3-4 Divide Decimals by 10, 100, and 1000 94
3-5 Divide Decimals by Whole Numbers 96
3-6 Patterns with Tenths, Hundredths, and Thousandths 98
3-7 Estimate Decimal Quotients 100
3-8 Decimal Divisors 102
3-9 Zeros in Division 104
3-10 Multiplication and Division Expressions 106
3-11 Evaluate Multiplication and Division Expressions 108
3-12 Round Quotients 110
3-13 Problem-Solving Strategy: Interpret the Remainder 112
3-14 Problem-Solving Applications: Mixed Review 114
End of Chapter Check Your Progress (Lessons 1–14) 116 Enrichment: Logic: Open and Closed Statements 117
Chapter 3 Test 118
Cumulative Review 119
Chapter Expressions and Equations Chapter Opener 121
4-1 Order of Operations 122
4-2 Translate Expressions 124
4-3 Evaluate Algebraic Expressions 126
4-4 Equations and Inequalities 128
4-5 Addition Equations 130
4-6 Subtraction Equations 132
4-7 Multiplication and Division Equations 134
4-8 Use Formulas 136
4-9 Explore Order of Operations with a Calculator 138
4-10 Problem-Solving Strategy: Use More Than One Step 140
4-11 Problem-Solving Applications: Mixed Review 142
End of Chapter Check Your Progress (Lessons 1–11) 144 Enrichment: Patterns: Sequences 145
Chapter 4 Test 146
Cumulative Review 147
Lesson promotes algebraic reasoning.
Trang 16Integers
Chapter Opener 149
5-1 Integers 150
5-2 Compare and Order Integers 152
5-3 Add Integers 154
5-4 Subtract Integers 156
5-5 Multiply Integers 158
5-6 Divide Integers 160
5-7 Integers and Order of Operations 162
5-8 Expressions and Equations with Integers 164
5-9 Temperature 166
5-10 Problem-Solving Strategy: Make a Table 168
5-11 Problem-Solving Applications: Mixed Review 170
End of Chapter Check Your Progress (Lessons 1–11) 172 Enrichment: Inequalities in One Variable 173
Chapter 5 Test 174
Cumulative Review 175
Chapter Number Theory and Fractions Chapter Opener 177
6-1 Divisibility 178
6-2 Prime and Composite Numbers 180 6-3 Prime Factorization 182
6-4 Equivalent Fractions 184
6-5 Greatest Common Factor 186
6-6 Fractions in Simplest Form 188
6-7 Mixed Numbers and Improper Fractions 190
6-8 Fraction Sense 192
6-9 Least Common Multiple 194
6-10 Compare Fractions 196
6-11 Order Fractions 198
6-12 Relate Fractions to Decimals 200
6-13 Rename Fractions as Decimals 202
6-14 Rename Decimals as Fractions 204
6-15 Terminating and Repeating Decimals 206
6-16 Rational Numbers 208
6-17 Compare and Order Rational Numbers 210
6-18 Problem-Solving Strategy: Find a Pattern 212
6-19 Problem-Solving Applications: Mixed Review 214
End of Chapter Check Your Progress (Lessons 1–19) 216 Enrichment: The Sieve of Eratosthenes 217 Chapter 6 Test 218
Cumulative Review 219
Trang 17Fractions: Addition and
Subtraction
Chapter Opener 221
7-1 Addition Properties: Fractions 222
7-2 Estimate Sums and Differences 224 7-3 Add Fractions 226
7-4 Add Mixed Numbers 228
7-5 Subtract Fractions 230
7-6 Subtract Mixed Numbers 232
7-7 Mental Math: Addition and Subtraction 234
7-8 Addition and Subtraction Expressions with Fractions 236
7-9 Addition and Subtraction Equations with Fractions 238
7-10 Problem-Solving Strategy: Work Backward 240
7-11 Problem-Solving Applications: Mixed Review 242
End of Chapter Check Your Progress (Lessons 1–11) 244 Enrichment: Logic: Statements and Negations 245
Chapter 7 Test 246
Cumulative Review 247
viii Chapter Fractions: Multiplication, Division, and Probability Chapter Opener 249
8-1 Multiply Fractions by Fractions 250
8-2 Multiply Fractions and Whole Numbers 252
8-3 Properties of Multiplication 254
8-4 Multiply Mixed Numbers 256
8-5 Meaning of Division 258
8-6 Divide Fractions by Fractions 260
8-7 Estimate Quotients of Fractions and Mixed Numbers 262
8-8 Divide with Whole and Mixed Numbers 264
8-9 Order of Operations with Fractions 266
8-10 Fractions with Money 268
8-11 Multiplication and Division Expressions with Fractions 270
8-12 Multiplication and Division Equations with Fractions 272
8-13 Probability 274
8-14 Compound Events 276
8-15 Permutations and Combinations 278 8-16 Predictions and Probability 280
8-17 Problem-Solving Strategy: Use a Diagram 282
8-18 Problem-Solving Applications: Mixed Review 284
End of Chapter Check Your Progress (Lessons 1–18) 286 Enrichment: Complex Fractions 287
Chapter 8 Test 288
Cumulative Review 289
Trang 18Data and Statistics
Chapter Opener 291
9-1 Surveys 292
9-2 Samples 294
9-3 Bias in Surveys 296
9-4 Record and Interpret Data 298
9-5 Apply Measures of Central Tendency and Range 300
9-6 Analyze Data 302
9-7 Box-and-Whisker Plots 304
9-8 Stem-and-Leaf Plots 306
9-9 Line Graphs 308
9-10 Double Line Graphs 310
9-11 Double Bar Graphs 312
9-12 Misleading Graphs and Statistics 314
9-13 Histograms 316
9-14 Interpret Circle Graphs 318
9-15 Problem-Solving Strategy: Make an Organized List 320
9-16 Problem-Solving Applications: Mixed Review 322
End of Chapter Check Your Progress (Lessons 1–16) 324 Enrichment: Triple Line and Bar Graphs 325
Chapter 9 Test 326
Cumulative Review 327
Chapter Geometry Chapter Opener 329
10-1 Measure and Draw Angles 330
10-2 Lines and Angles 332
10-3 Angle Pairs 334
10-4 Angles of Parallel Lines 336
10-5 Line Constructions 338
10-6 Constructions with Angles 340
10-7 Polygons 342
10-8 Triangles 344
10-9 Quadrilaterals 346
10-10 Angles of Triangles and Quadrilaterals 348
10-11 Angles of Polygons 350
10-12 Circles 352
10-13 Congruent and Similar Polygons 354
10-14 Transformations 356
10-15 Symmetry 358
10-16 Tessellations 360
10-17 Solid Figures 362
10-18 Views of Solid Figures 364
10-19 Problem-Solving Strategy: Logical Reasoning 366
10-20 Problem-Solving Applications: Mixed Review 368
End of Chapter Check Your Progress (Lessons 1–20) 370 Enrichment: Networks 371
Chapter 10 Test 372
Cumulative Review 373
Trang 19Ratio, Proportion,
and Percent
Chapter Opener 375
11-1 Ratio 376
11-2 Equivalent Ratios 378
11-3 Rates 380
11-4 Proportions 382
11-5 Solve Proportions 384
11-6 Write Proportions 386
11-7 Proportions and Similar Figures 388
11-8 Use Proportions 390
11-9 Scale Drawings and Maps 392
11-10 Relate Percents to Fractions 394
11-11 Relate Percents to Decimals 396
11-12 Decimals, Fractions, and Percents 398
11-13 Percents Greater Than 100% 400
11-14 Percents Less Than 1% 402
11-15 Problem-Solving Strategy: Combine Strategies 404
11-16 Problem-Solving Applications: Mixed Review 406
End of Chapter Check Your Progress (Lessons 1–16) 408 Enrichment: Pythagorean Theorem 409
Chapter 11 Test 410
Cumulative Review 411
Chapter Percent Applications Chapter Opener 413
12-1 Mental Math: Percent 414
12-2 Percent Sense 416
12-3 Percentage of a Number 418 12-4 Find the Rate 420
12-5 Find the Original Number 422 12-6 Percent Problems 424
12-7 Discount and Sale Price 426
12-8 Sales Tax and Total Cost 428 12-9 Better Buy 430
12-10 Commission 432
12-11 Simple Interest 434
12-12 Make Circle Graphs 436
12-13 Problem-Solving Strategy: Write an Equation 438
12-14 Problem-Solving Applications: Mixed Review 440
End of Chapter Check Your Progress (Lessons 1–14) 442 Enrichment: Percent Change 443
Chapter 12 Test 444
Cumulative Review 445
x
*
*Develops concept or skill with manipulatives Lesson promotes algebraic reasoning.
Trang 20More Concepts in
Chapter Opener 495
14-1 Two-Step Equations 496
14-2 Addition and Subtraction Equations with Integers 498
14-3 Multiplication and Division Equations with Integers 500
14-4 Functions and Ordered Pairs 502
14-5 Graph Ordered Pairs 504
14-6 Graph Reflections and Translations 506
14-7 Graph Rotations 508
14-8 Graph Functions 510
14-9 Algebraic Patterns 512
14-10 Problem-Solving Strategy: Use More Than One Strategy 514
14-11 Problem-Solving Applications: Mixed Review 516
End of Chapter Check Your Progress (Lessons 1–11) 518 Enrichment: Slope 519
Chapter 14 Test 520
End-of-Book Materials Still More Practice 521
Brain Builders 533
Mental Math 537
Glossary 546
Index 553
Symbols and Formulas 563
Table of Measures 564
Chapter Measurement Chapter Opener 447
13-1 Measure Metric Length 448
13-2 Measure Metric Capacity and Mass 450
13-3 Measure Customary Length 452
13-4 Measure Customary Capacity and Weight 454
13-5 Compute Customary Units 456
13-6 Compute with Time 458
13-7 Relate Customary & Metric Units 460 13-8 Perimeter 462
13-9 Area of Rectangles and Squares 464
13-10 Area of Triangles and Parallelograms 466
13-11 Area of Trapezoids 468
13-12 Circumference 470
13-13 Area of a Circle 472
13-14 Surface Area of Cubes, Rectangular Prisms, and Cylinders 474 13-15 Surface Area of Pyramids and Triangular Prisms 476
13-16 Volume of Prisms 478
13-17 Volume of Triangular Prisms and Cylinders 480
13-18 Volume of Pyramids 482
13-19 Use Formulas to Solve Problems 484
13-20 Problem-Solving Strategy: Use Drawings / Formulas 486 13-21 Problem-Solving Applications: Mixed Review 488
End of Chapter Check Your Progress (Lessons 1–21) 490 Enrichment: Logic: Conjunctions and Disjunctions 491
Chapter 13 Test 492
Trang 21Progress in Mathematicsincludes a
“handbook” of essential skills, Skills Update,
at the beginning of the text These one-page
lessons review skills you learned in previous
years It is important for you to know this
content so that you can succeed in math
this year
If you need to review a concept in Skills
Update, your teacher can work with you,
using manipulatives, which will help
you understand the concept better
The Skills Update handbook can be used
throughout the year to review skills you
may already know Since many lessons
in your textbook refer to pages in the Skills Update, you can use a particularlesson at the beginning of class as a warm-up activity Or your class maychoose to do the Skills Update lessons at the beginning of the year so thatyou and your teacher can assess your understanding of these previouslylearned skills
You may even want to practice specific skills at home
If you need more practice than what is provided onthe Skills Update page, you can use the practicepages available online atwww.sadlier-oxford.com.These practice pages have an abundance ofexercises for each one-page lesson
A Review of Mathematical
Skills from Grade 5
Trang 22Whole Numbers: Place Value, Compare, and Order
Name the period of the underlined digits.
39,63019,578
130,43436,415
3 3and 1 3
19,578 is least
6 936,415 39,630
39,630
19,578130,434
36,415
The value of each digit in a number depends on its place in the
number Each place is 10 times the value of the next place to its right
The 4 in 74 is in the ones place Its value is 4 ones, or 4.
The 4 in 741 is in the tens place Its value is 4 tens, or 40.
The 4 in 7415 is in the
hundreds place Its value
is 4 hundreds, or 400.
To compare and order whole numbers:
Align the digits by place value
Compare the digits in each place, starting with the greatest place
In order from greatest to least, the numbers are:
130,434; 39,630; 36,415; 19,578
Millions Period
Thousands Period
Ones Period
hundredstens ones hundredstens ones hundredstens ones
Trang 23Round Whole Numbers
The population of Midway is 83,524 Since
populations change frequently, a rounded number
may be used instead of the exact number
To round a number to a given place:
Find the place you are rounding to
Look at the digit to its right
If the digit is less than 5, round down.
If the digit is 5 or greater, round up.
Round 83,524 to the nearest ten
83,524 The digit to the right is 4
4 583,520 Round down to 83,520
Round 83,524 to the nearest hundred
83,524 The digit to the right is 2
2 5
83,500 Round down to 83,500
Round 83,524 to the nearest thousand
83,524 The digit to the right is 5
5 5
84,000 Round up to 84,000
Round each to the nearest ten, hundred, and thousand.
Use a number line to help you
Trang 24Factors, Multiples, and Divisibility
3 0 0 3 4 12 3 8 24
Factors are numbers that are multiplied to find a product
To find all the factors of a number,
use multiplication sentences
Find all the factors of 20
A number is divisible by another number when you divide
and the remainder is zero
List all the factors of each number.
Divisibility by 10
A number is divisible by
10 if its ones digit is 0
40, 280, 500, 2070, and46,790are divisible by 10.All even numbers are divisible by 2
Trang 25Read each decimal Then write the place of the underlined
digit and its value.
The value of a digit in a decimal depends on its
position, or place, in the decimal Each place is
10 times the value of the next place to its right
The 4 is in the ones place.
Its value is 4 ones, or 4.
The 4 in 0.4 is in the tenths place.
Its value is 4 tenths, or 0.4.
The 4 in 0.04 is in the hundredths place Its value is 4 hundredths, or 0.04.
To read a decimal less than 1:
Start at the decimal point
Read the number as a
whole number Then saythe name of the place
Study this example.
37.19
Read: thirty-seven and nineteen hundredths
0 4 4 0
0 0 0
HundredsTens Ones Tenths Hundredths
Trang 26Add Whole Numbers and Decimals
Add: 8164 4676
First estimate by rounding: 8000 5000 13,000 Then add
To add whole numbers:
Add the ones Add the tens Add the Add the thousands.Regroup Regroup hundreds Regroup
8 1 6 4 8 1 6 4 8 1 6 4 0 8,1 6 4
4 6 7 6 4 6 7 6 4 6 7 6 0 4,6 7 6
0 0 0 0 0 0 4 0 0 8 4 0 1 2,8 4 0The sum is 12,840
?
Think12,840 is close to theestimate of 13,000
Think1.59 is close to the estimate of 1.6
Add: 0.44 0.3 0.85
First estimate by rounding to the nearest tenth: 0.4 0.3 0.9 1.6 Then add
To add decimals:
decimal points if necessary decimal point
Trang 27Subtract Whole Numbers and Decimals
Subtract: 4816 1932
First estimate by rounding: 5000 2000 3000 Then subtract
To subtract whole numbers:
Subtract More tens needed
More hundreds
Subtract thethe ones Regroup Subtract
needed Regroup
thousands.Subtract
?
Think
2884 is close to theestimate of 3000
?
Think0.24 is close to theestimate of 0.2
Estimate by rounding Then subtract.
1. 489 2. 6244 3. 36,243 4. 456,781 5. 587,893
366 0029 13,963 179,660 498,721
6. 0.74 7. 0.81 8. $.95 9. $14.97 10 0.8 0.29
Trang 28Inverse Operations: Addition and Subtraction
Inverse operations are mathematical
operations that undo each other.
Addition and subtraction are inverse operations
Let a, b, and c be any numbers.
If a b c, then c b a If c b a, then a b c.
Subtraction “undoes” addition Addition “undoes” subtraction
Find the missing number
Find the missing number
Multiplication and division are also inverse operations
Let a, b, and c be any numbers.
If a b c, then c b a If c b a, then a b c.
Division “undoes” multiplication Multiplication “undoes” division
Find the missing number
Find the missing number
Find the missing number using inverse operations.
1 8 a 12 2 36 b 9 3 r $2.96 $10.00
4 n 40 56 5 19 d 418 6 y 3 233
Trang 29Properties of Addition and Multiplication
The following properties of addition and multiplication
are true for any numbers a, b, and c.
Changing the order of the addends
does not change the sum
abba
5995
14 14
Changing the order of the factors
does not change the product
Changing the grouping of the addends
does not change the sum
(ab)ca (bc)
(14)71 (47)
5 7 1 11
12 12
Changing the grouping of the factors
does not change the product
(ab)ca (bc)(65)26 (52)
30 2 6 10
60 60
Think
“grouping”
The sum of zero and a number
is that number
a0 a 0 a a
890 89 0 89 89
The product of zero and a number is zero
0 a 0 a0 0
0 33 0 330 0
The product of one and a number
Trang 30Multiply 1- and 2-Digit Numbers
Multiply: 7 27
First estimate by rounding: 7 30 210
Then multiply
To multiply by a one-digit number:
Multiply the ones Multiply the tens
Then regroup Then regroup
Think
1472 is close to theestimate of 1500
?
Estimate by rounding Then find the poduct.
1. 55 2. 613 3 7 $8.64 4. 67 5. 329 6 92 $7.68
Trang 31Follow these steps to divide:
Decide where to begin 4 621 38 46 218the quotient
The quotient begins in the tens place
Estimate. Think: 4 62 183 4 21 Try 5
0 0 2 1
Check. 46 47 2162 2162 21 2183
Estimate to find the missing digit in the quotient.
Complete the division.
Trang 32Divide Whole Numbers
Divide: 4782 83
Estimate by using compatible numbers: 4800 80 60
Decide where to begin the quotient.
8 347 28 83 478The quotient begins in the tens place
The quotient is 57 R51
Study these examples.
Estimate by using compatible numbers Then find the quotient.
ThinkEstimate:
$.90 3 $.30
ThinkEstimate:
$4.00 20 $.20
Trang 33Add and Subtract Fractions: Like Denominators
To add fractions with like denominators:
Add the numerators 28 4
2 2
3
4 simplest form
Study these examples.
1
7 0
2
1 4
2
2 4
1
2 2
11
2 2
To subtract fractions with like denominators:
Subtract the numerators
Write the result over the
2 8
4 8
6 8
3 8
8
7 8
1 8
2 8
4 8
6 8
3 8
8
7 8GCF of 6 and 8: 2
GCF of 2 and 8: 2
Trang 34Make Pictographs
Solve Use the pictograph above.
many symbols were used for needed so that Jazz and R&B R&B? for Jazz? would have the same number?
sold in all? How can you use 100 CDs and 200 CDs?
multiplication to help you answer?
5 Make a pictograph using the same
data from Al’s Audio Outlet Change the key so that each symbol represents
10 CDs How does this change the pictograph? What would it look like if each represented 100 CDs?
RockClassicalFolkR&BJazzWorld Music
Category Number Sold
CDs Sold at Al’s Audio Outlet
You can make a pictograph to
display the data in the table
To make a pictograph:
List each category of music
Choose a symbol or picture touse to represent a number of CDssold Examine your data Select
a convenient value for the symbol
Let 50 CDs
Draw the symbols to representthe data Round data to helpyou do this For example:
391 400 247 250
Write a key to show the value
of the symbol used
Give your graph a title
Trang 35Make Bar Graphs
Henry displayed the data at the
right in a horizontal bar graph
To make a horizontal bar graph:
Draw horizontal and vertical axes
on grid paper
Use the data from the table to choose
an appropriate scale (The data rangefrom 26 to 82 Choose intervals of 10.)
Draw and label the scale along the
horizontal axis Start at 0 andlabel equal intervals
Label the vertical axis List
the name of each dinosaur
Draw horizontal bars to
represent each length
Make the bars of equalwidth
Write a title for your graph
To make a vertical bar graph, place the scale along the
vertical axis and the items along the horizontal axis
Solve Use the bar graph above.
axis? the horizontal axis? between 30 and 40 feet?
3 Make a horizontal or vertical bar graph using the data
on lengths of dinosaurs Change the scale to represent 20-ft intervals
Albertosaurus 26 ft
Brachiosaurus 52 ftTyrannosaurus 39 ftUltrasaurus 82 ft
Lengths of Some Dinosaurs
Trang 36Equally/Not Equally Likely Outcomes
For each experiment, list the possible outcomes Then write
whether the outcomes are equally likely or not equally likely.
on the board
1 white, 1 yellow, and 1 blue
Choose a ball without looking
Use the spinner on the right to find
the probability of landing on:
6
5 3
B
19
357
A BC
1 2
3 4
For each of the spinners, there are 5 possible results,
or outcomes: 1, 3, 5, 7, 9
With Spinner A, each number has the same
chance of occurring The outcomes are equally likely
With Spinner B, the outcomes are not equally likely
The spinner is more likely to land on 1 than on 9
The spinner has 8 equal sections Of the equal
sections, 3 are red, 3 are green, and 2 are blue
The probability of the spinner landing on
red is 3 out of 8
green is 3 out of 8
blue is 2 out of 8
19
357
A
Trang 37List Outcomes
Make a list of all possible outcomes for each experiment.
Then write the total number of outcomes.
1 toss a coin and toss a 2 toss a coin and spin the spinner
green/red counter
3 pick a card without looking 4 spin the spinner and pick a cube
and roll a number cube without looking
1 4 6 2 3 4
1
5 6
Yes No
Spinner 1
3 1
2
Spinner 2
2143
312
You can make an organized list to show all possible
outcomes of an experiment
In an experiment, Sandra spins the two given
spinners Find all possible outcomes How many
possible outcomes are there?
Look at the spinners to find the possible outcomes
Spinner 1: Blue (B), Red (R), or Green (G)
Spinner 2: 1, 2, or 3
Make an organized list of the possible pairs of
outcomes Then count the number of outcomes
Blue (B) - 1 Red (R) - 1 Green (G) - 1
Blue (B) - 2 Red (R) - 2 Green (G) - 2
Blue (B) - 3 Red (R) - 3 Green (G) - 3
So there are 9 possible outcomes
Trang 38P
X
E Q
Some simple geometric figures:
point — an exact location in space,
usually represented by a dot
line — a set of points in a plane that
forms a straight path and extends indefinitely in opposite directions
line segment — part of a line with
two endpoints
plane — a flat surface that extends
indefinitely in all directions
ray — part of a line that starts at an
endpoint and extends indefinitely in one direction
angle — formed by two rays with a common
endpoint The common endpoint iscalled the vertex of the angle The letter naming the vertex is always
Trang 39Lines: Intersecting and Parallel
Lines in the same plane either intersect (meet at a point)
or are parallel (never meet)
KL and UV are intersecting lines QR and ST are parallel lines.
They meet at point P QR ST
Line segments and rays may also intersect or be parallel
Draw each You may use dot paper.
9 ACintersecting DE at point M 10 3 lines intersecting at point B
means “is parallel to.”
Trang 40A polygon is a closed plane figure formed
by line segments that intersect only at their
endpoints The line segments are the sides
of the polygon
The point where any two sides of a polygon
meet is called a vertex (plural: vertices)